On lifespan of solutions to the Einstein equations (Q2466988)

Consider the initial value problem \(G_{\mu\nu}=T_{\mu\nu},\;g_{\mu\nu| x^0=0}=g^0_{\mu\nu}, \;{{\partial g_{\mu\nu}}\over{\partial x^0}}_{| x^0=0}=g^1_{\mu\nu}\), where \(G_{\mu\nu}, \mu,\nu =0,1,2,3\) is the Einstein tensor and \(T_{\mu\nu}\) is the energy-momentum tensor. The author studies the existence of the maximal solutions of this system for a suitable large class of initial data. He concentrates outside of the cone of influence of possible singularities. He obtains information about the asymptotic behavior of metric coefficients and about the domain \(\mathcal{U}\) where the solutions of the problem are well defined. The obtained results are improvements of those from \textit{D. Christodoulou, N. O'Murchadha}, ``The boost problem in general relativity,'' Commun. Math. Phys. 80, 271--300 (1980; Zbl 0477.35081)].